Global Stability Analysis of Disease Free Equilibrium for Modeling the Dynamics of Bacteria Infection in Higher Institution Kaura Namoda, Nigeria

Abstract

Bacterial infection of the intestine is caused by ingestion of food or water containing vibrio cholera. Sanitary conditions in the environment play an important role. In this research work, we proposed a model to describe the transmission of the bacterial infection amongst the Students of Federal Polytechnic Kaura Namoda, Zamfara State. We also incorporated the effectiveness of drug usage and awareness for proper hygiene and sanitation. We obtained the invariant region and found that the model system is well posed mathematically and epidemiologically. The disease free occurs when the infection is free in the population or no epidemic in the population, while, endemic equilibrium occurs when the infection is persistence in the population. So, disease free and endemic equilibrium were determined. The effective reproduction number  is obtained and we established that disease free equilibrium is globally asymptotically stable if secondary case of the infection on average is less than a Unit (), using suitable Lyapunov function method. Numerical simulations from figures show that Hygiene and Sanitation awareness, and Effectiveness of drug reduced the average number of the secondary cases of bacterial infection disease; on the other hand, Production of Bacterial infection, Human population and Contact rate increased the average number of the secondary case of the bacterial infection disease.